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Determine the length of AB and AD sides from ABCD parallelogram with AD = 3/5AB  if...

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landishigh | Student, College Freshman | (Level 1) Honors

Posted September 28, 2010 at 10:00 PM via web

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Determine the length of AB and AD sides from ABCD parallelogram with AD = 3/5AB  if ABCD's perimeter is 11.2.

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giorgiana1976 | College Teacher | (Level 3) Valedictorian

Posted September 28, 2010 at 10:12 PM (Answer #1)

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ABCD is a parallelogram, so the opposite sides are equal and parallel.

AB=CD

AD=BC

AD=(3/5)AB

P=2AB+2AD=2(AB+AD)=2[AB+(3/5)AB]

11.2cm=2[AB+(3/5)AB]

5.6cm=AB+(3/5)AB

We note that we'll have to have the same denominator on both sides of equality, the denominator being 5.

5*5.6cm= 5*AB + 3*AB

28cm=8AB

AB=7/2cm

AB=3.5cm

AD= (3/5)AB

AD= (3/5)*3.5

AD=2.1cm

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pohnpei397 | College Teacher | (Level 3) Distinguished Educator

Posted September 28, 2010 at 10:12 PM (Answer #2)

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The answer to this is that AB is 3.5 and AD is 2.1.  Here is how to find this.

We know that the perimeter of the parallelogram can be found by multiplying both sides by 2 and then adding the products.

We know then that two sides are equal to 2AB.

And we know that the other two sides are equal to 6/5 AB.

So now we can say that

2AB + 6/5AB = 11.2

This means that

3.2AB = 11.2

When we divide this, we find that

AB = 3.5

To find AD, we do the following:

AD = 3/5(3.5)

This multiplies out to

AD = 2.1

 

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neela | High School Teacher | (Level 3) Valedictorian

Posted September 28, 2010 at 10:37 PM (Answer #3)

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ABCD is a parallelogram. AD = (3/5)AB

The perimeter is 1.2.

To determine AB and AD.

Solution:

Let AB =x .

Then AD = (3/5)x = 0.6x.

Since ABCD is a parallelogram AB = CD and AD = BC.

Therefore , the perimeter p = 2x+2*0.6x = 3.2x which is equal to 11.2.

So 3.2x = 11.2

x = 11.2/3.2 = 3.5.

So AB = 3.5.

Therefore AD = (3/5)AD = 3*3.50/5 = 2.1.

 

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william1941 | College Teacher | (Level 3) Valedictorian

Posted September 28, 2010 at 10:10 PM (Answer #4)

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For a parallelogram the opposite sides are equal. So here we have AB = DC and AD = BC.

Now we know that AD = (3 / 5)* AB. And the perimeter of the parallelogram is 11.2.

AB + BC + CD + DA = 11.2

=> AB + (3 / 5)* AB + AB + (3 / 5)* AB = 11.2

=> AB *( 1+ 3/5 +1 + 3/5) = 11.2

=> AB = 11.2 / 3.2

=> AB = 3.5

AD = (3 / 5)* AB

=> AD = (3 / 5)* 3.5 = 2.1

Therefore AB is 3.5 and AD is 2.1

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